Question

5/x= 6/x-1/3

Answer 1

\[\frac{ 5 }{ x }=\frac{ 6 }{ x}-\frac{ 1 }{ 3 }\]

Answer 2

simplify the equation first by multiplying by the reciprocals

Answer 3

18-x/3x

Answer 4

try multiplying the
WHOLE equation
by the reciprocal of 1/ x

Answer 5

can you draw it out cuz im a little confused?

Answer 6

x 5 6 1
--- [ --- = --- - --- ]
1 x x 3

Answer 7

thats how it would look
then you can cancel out numbers, varables etc and simplify

Answer 8

\[\frac{ 5x }{ x}=\frac{ 6x }{ x }-\frac{ x }{ 3 }\]

Answer 9

yep

Answer 10

now what do i do after that?

Answer 11

cancel :O

Answer 12

cancel what? if itn's not times i thought you can't cancel?

Answer 13

\[\frac{5}{x}-\left(-\frac{1}{3}+\frac{6}{x}\right)=0\]\[\frac{x-3}{3 x}=0 \]x = 3

Answer 14

12345 qwert 12345
--------- ------
19 qwert 19

Answer 15

it is a essentially a multiplication problem

5 x
--- . --- you are multiply by the reciprocal
x 1

Answer 16

you cancel out a term

Answer 17

x but that leaves you with 5 and the answer in my book is 3?

Answer 18

youre not done yet -.-

Answer 19

ok, sorry i'm confused, did you go back?

Answer 20

on simplification yes

Answer 21

anyways simplify the whole equation just to make it look easier to solve

Answer 22

\[\frac{5}{x} = \frac{6}{x} -\frac{1}{3}\]multiply everything by \(x\)
\[5 = 6 - \frac{x}{3}\]subtract 6 from both sides
\[-1=-\frac{x}{3}\]multiply both sides by -3
\[3 = x\]

Answer 23

Check:\[\frac{5}{3} = \frac{6}{3} - \frac{1}{3} \]\[\frac{5}{3} = \frac{6-1}{3} = \frac{5}{3}\checkmark \]

Answer 24

ahhhh that makes sense

Answer 25

that's always the goal :-)

Answer 26

how did you know to multiply it by x, i have alot of problems like this so i'm just wondering

Answer 27

you could also say that given the numerators show 5 = 6 - 1, that x must = 3 so the denominators are equal...

Answer 28

oh, when faced with fractions, multiply by the denominators to get rid of the fractions.

Answer 29

we could have multiplied by 3x here and done it all in one step:

\[\frac{5}{x} = \frac{6}{x} - \frac{1}{3} \]multiply by \(3x\)
\[3x*\frac{5}{x} = 3x*\frac{6}{x} - 3x*\frac{1}{3}\]\[15 = 18-x\]\[-3 = -x\]\[x = 3\]

Answer 30

ah, ok thank you very much!

Answer 31

good luck!